High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ If [tex]f(4) = 246.4[/tex] when [tex]r = 0.04[/tex] for the function [tex]f(t) = P e^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 50
B. 210
C. 289
D. 1220

Answer :

To solve for the value of [tex]\( P \)[/tex] in the function [tex]\( f(t) = P e^{rt} \)[/tex], use the given information [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex].

1. First, write down the equation with the known values:
[tex]\[
f(4) = P \cdot e^{0.04 \times 4}
\][/tex]

2. Substitute the given value for [tex]\( f(4) \)[/tex]:
[tex]\[
246.4 = P \cdot e^{0.16}
\][/tex]

3. Calculate [tex]\( e^{0.16} \)[/tex]. From a calculation, we know:
[tex]\[
e^{0.16} \approx 1.1735
\][/tex]

4. Substitute this value back into the equation:
[tex]\[
246.4 = P \cdot 1.1735
\][/tex]

5. Solve for [tex]\( P \)[/tex] by dividing both sides by [tex]\( 1.1735 \)[/tex]:
[tex]\[
P \approx \frac{246.4}{1.1735} \approx 209.97
\][/tex]

6. Round [tex]\( P \)[/tex] to the nearest whole number for the multiple-choice answer:
[tex]\[
P \approx 210
\][/tex]

Therefore, the approximate value of [tex]\( P \)[/tex] is 210. The correct answer is B. 210.